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This 2 page Class Notes was uploaded by Mrs. Haley Hartmann on Monday October 5, 2015. The Class Notes belongs to MTH151 at Central Michigan University taught by TiborMarcinek in Fall. Since its upload, it has received 7 views. For similar materials see /class/218897/mth151-central-michigan-university in Mathematics (M) at Central Michigan University.
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Date Created: 10/05/15
Pagel Tibor Marcinek Handoutfor MTH 151 Problem Solving Problem solving Steps and Strategies Problem Solving means engaging in a task for which the solution method is not known in advance NCTM s Standards 2000 In this sense a problem is an opposite to routine in which solution method is known from the very beginning A problem is a relative concept Add 6 and 7 is obviously a routine task for us but it may become a problem for a first grader What does it take to succeed in solving a routine task Follow all steps of your procedure and make sure you won t make a mistake Concentration is the main factor What does it take to succeed in problem solving Well the answer is much more complex To be a successful problem solver you 1 MUST BE ACTIVE and PERSISTENT Guess check suggest test experiment draw pictures set up equations try to organize information in tables etc If you get stuck DON T take it as a signal to give up Take it as a signal to change your point of view try another strategy or organize information differently 2 MUST HAVE SOME EXPERIENCE The more experience with problem solving you have the better are your odds to solve your next problem Good intuition and luck go hand in hand with experience Don t avoid problems they help you to become a better problem solver 3 MUST HAVE SOME KNOWHOW quotmaster your craft In math you can set up a perfect equation to solve your problem but it is of a little use unless you know how to solve it The following page summarizes steps in problem solving It comes from G Polya and is based on experience of many successful problem solvers By no means it is an algorithm You cannot follow it step by step and expect to solve your problem It is meant to help you to quotget off the mark Anytime you get stuck try to go over the questions on the sheet They may help you to find a different perspective Step 2 Devising a plan is a very important step and contains different problem solving strategies A mathematics or elementary teacher must have a solid arsenal of problem solving strategies This part of the course should give you opportunity to experience some of them Sources Process Standards of NCTM s Principles and Standards for School Mathematics 2000 G Polya quotHow to Solve Itquot 2nd ed Princeton University Press 1957 Hecht T Sklenarikova 2 Methods of Solving Math Problems In Slovak only PageZ Tibor Marcinek Handoutfor MTH 151 Problem Solving Four steps of problem solving by Polya 1 Understand the problem 0 Do you understand all words 0 What are you asked to find out or show 0 Can you restate the problem in your own words 0 What is unknown Which are unknowns 0 List all information the problem provides Is any information missing Is any information redundant 0 Can you draw a picture or diagram to help you understand the problem 0 Can you work out some numerical examples that would help make the problem more clear 2 Devise a plan Problem Solving Strategies 0 Guess and check 0 Look for a system 0 Solve a simpler problem or a special case of the original problem 0 Solve a related problem 0 Make an organized list List all possibilities 0 Draw a picture or diagram tree diagram Venn diagrams 0 Look for a pattern 0 Work backwards 0 Make a table 0 Use deduction 0 Use a variable Set up an equation 0 Experiment Act it out 3 Carry out the plan 0 Be patient most problems are not solved quickly nor on the first attempt 0 Allow yourself a reasonable amount of time to solve the problem If you are not successful ask for help or put the problem aside for a while Inspiration comes even when you do not expect it o If a plan does not work immediately be persistent 0 Do not let yourself get discouraged by starting over several times A new beginning often brings a better strategy and increased odds to solve the problem 0 If a strategy you chose does not work out don t forget to change your point of view and try another strategy 4 Look back reflect 0 Does your answer make sense Did you answer all of the questions 0 What did you learn by doing this 0 Could you have done this problem another way using a different strategy 0 Can you see a simpler solution 0 Can you generalize your solution Can you make it a routine
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